Question

For the year 2009, the table below gives the percent of people living below the poverty line in the 26 states east of the Mississippi River. Answer the following questions based on this data. State Percent Alabama 7.5 Connecticut 7.9 Delaware 14.9 Florida 13.2 Georgia 12.1 Illinois 10.0 Indiana 9.9 Kentucky 11.9 Maine 13.3 Maryland 10.9 Massachusetts 7.9 Michigan 15.8 Mississippi 9.1 State Percent New Hampshire 14.6 New Jersey 8.3 New York 9.1 North Carolina 12.1 Ohio 13.6 Pennsylvania 10.5 Rhode Island 8.2 South Carolina 12.5 Tennessee 10.0 Vermont 7.3 Virginia 10.4 West Virginia 10.5 Wisconsin 16.1 Find the five-number summary for this data.

Answer 1

Five point summary

We get the data as:

STATE	% OF PEOPLE
State Percent Alabama	7.5
Connecticut	7.9
Delaware	14.9
Florida	13.2
Georgia	12.1
Illinois	10
Indiana	9.9
Kentucky	11.9
Maine	13.3
Maryland	10.9
Massachusetts	7.9
Michigan	15.8
Mississippi	9.1
State Percent New Hampshire	14.6
New Jersey	8.3
New York	9.1
North Carolina	12.1
Ohio	13.6
Pennsylvania	10.5
Rhode Island	8.2
South Carolina	12.5
Tennessee	10
Vermont	7.3
Virginia	10.4
West Virginia	10.5
Wisconsin	16.1

We know that five point summary consists of minimum, maximum, median, Q1 and Q3.

To do the summary we have to sort the data firstly. After sorting we get:

7.3
7.5
7.9
7.9
8.2
8.3
9.1
9.1
9.9
10
10
10.4
10.5
10.5
10.9
11.9
12.1
12.1
12.5
13.2
13.3
13.6
14.6
14.9
15.8
16.1

Thus the minimum is 7.3 and maximum is 16.1.

As there are 26 data points median will be the mean of 13th and 14th observation.

So the median is: (10.5+10.5)/2 = 10.5.

Now Q1 and Q3 are respectively the midpoints of the two sides of the median.

We can write as:

(7.3,7.5,7.9,7.9,8.2,8.3,9.1,9.1,9.9,10,10,10.4,10.5) | (10.5,10.9,11.9,12.1,12.1,12.5,13.2,13.3,13.6,14.6,14.9,15.8,16.1)

So Q1= 9.1 and Q3= 13.2.